Finite Group Databasebeta

← #29721401

Subgroups — #29721401

Order 15616.

738 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840066C211yesmaximal, characteristic, complemented
2C2×#16839822C211yesmaximal, characteristic
3#21451650C211yesmaximal, characteristic
4#21448502C211yesmaximal, characteristic
5#21447257C211yesmaximal, characteristic
6#21447246C211yesmaximal, characteristic
7#21447025C211yesmaximal, characteristic
8#21447025C211yesmaximal, characteristic
9#21446577C211yesmaximal, characteristic, complemented
10#21446556C211yesmaximal, characteristic, complemented
11#21446551C211yesmaximal, characteristic, complemented
12#21446507C211yesmaximal, characteristic, complemented
13#21446493C211yesmaximal, characteristic, complemented
14#21445825C211yesmaximal, characteristic, complemented
15C61×#1989C211yesmaximal, characteristic, complemented
16C2×#14519757C2211yescharacteristic
17C2×C4×Dic122C2211yescharacteristic
18C2×#14519734C2211yescharacteristic
19#16840066—24no—
20#16839822—24no—
21C2×#14519710C2211yescharacteristic
22C2×#14519710C2211yescharacteristic
23C2×#14519710C2211yescharacteristic
24C2×#14519708C2211yescharacteristic
25C2×C4⋊#92418C2211yescharacteristic
26C2×#14519702C2211yescharacteristic
27C2×#14519702C2211yescharacteristic
28C2×#14519700C2211yescharacteristic
29C2×#14519700C2211yescharacteristic
30C2×#14519689C2211yescharacteristic
31C2×#14519689C2211yescharacteristic
32C2×#14519687C2211yescharacteristic
33C2×C8×Dic61C2211yescharacteristic
34#16839695—21no—
35#16839695—21no—
36#16839684—21no—
37#16839684—21no—
38#16839667C2211yescharacteristic
39#16839661C2211yescharacteristic
40#16839660—21no—
41#16839658C2211yescharacteristic
42#16839658C2211yescharacteristic
43#16839654—21no—
44#16839653—21no—
45#16839647—21no—
46#16839632C2211yescharacteristic
47#16839619C2211yescharacteristic
48#16839619C2211yescharacteristic
49#16839619C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839525C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54C2×#125×C61C2211yescharacteristic
55C2×C4⋊C8×C61C2211yescharacteristic
56C4×C4⋊C4×C61C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#340C2211yescharacteristic
59C61×#340C2211yescharacteristic
60C61×#340C2211yescharacteristic
61C22×Dic122C2311yescharacteristic
62C22×C4×D61C2311yescharacteristic
63C22×#92418C2311yescharacteristic
64C22×#92418C2311yescharacteristic
65#14519757—22no—
66#14519757—22no—
67C4×Dic122—22no—
68C4×Dic122—22no—
69#14519734—22no—
70#14519734—22no—
71C2×C4⋊Dic61—21no—
72C2×C4⋊Dic61—21no—
73C2×C4⋊Dic61—21no—
74C2×C4⋊Dic61—21no—
75C2×C4⋊Dic61C2311yescharacteristic
76C2×C4⋊Dic61C2311yescharacteristic
77C2×C4⋊Dic61C2311yescharacteristic
78C2×#11758196—21no—
79C2×#11758196—21no—
80C2×#11758196—21no—
81C2×#11758196D411yescharacteristic
82C2×#11758196D411yescharacteristic
83C2×#11758198—21no—
84C2×#11758198—21no—
85C2×#11758198—21no—
86C2×#11758198—21no—
87C2×#11758198D411yescharacteristic
88C2×#11758198D411yescharacteristic
89C2×C4×Dic61—21no—
90C2×C4×Dic61C2311yescharacteristic
91#14519710—22no—
92#14519710—22no—
93#14519710—22no—
94#14519708—22no—
95C4⋊#92418D414yes—
96#14519702—22no—
97#14519702—22no—
98#14519700—22no—
99#14519700—22no—
100#14519689—22no—
101#14519689—22no—
102#14519687—22no—
103C8×Dic61—22no—
104#14519684—21no—
105#14519684—21no—
106#14519684—21no—
107#14519684—21no—
108#14519684—21no—
109#14519684—21no—
110#14519684—21no—
111#14519684—21no—
112C22×C8×C61C2311yescharacteristic
113C22×C8×C61C2311yescharacteristic
114#125×C61—22no—
115#125×C61—22no—
116C2×C4⋊C4×C61—21no—
117C2×C4⋊C4×C61—21no—
118C2×C4⋊C4×C61C2311yescharacteristic
119C2×C4⋊C4×C61C2311yescharacteristic
120C2×C4⋊C4×C61C2311yescharacteristic
121C2×C4⋊C4×C61C2311yescharacteristic
122C2×C42×C61—21no—
123C2×C42×C61C2311yescharacteristic
124C4⋊C8×C61—22no—
125#95×C61—21no—
126C23×D61C2×D411yescharacteristic
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61—21no—
131C22×C4×C61C2×D411yescharacteristic
132C22×C4×C61C2×D411yescharacteristic
133C22×C4×C61C2411yescharacteristic
134C22×Dic61—21no—
135C22×Dic61—21no—
136C22×Dic61—21no—
137C22×Dic61—21no—
138C22×Dic61C2×D411yescharacteristic
139C22×Dic61C2×D411yescharacteristic
140C22×Dic61C2×D411yescharacteristic
141C2×C4×D61—21no—
142C2×C4×D61—21no—
143C2×C4×D61—21no—
144C2×C4×D61—21no—
145C2×C4×D61—21no—
146C2×C4×D61—21no—
147C2×Dic122—21no—
148C2×Dic122—21no—
149C2×Dic122—21no—
150C2×Dic122—21no—
151C2×Dic122—21no—
152C2×Dic122#4112yes—
153C2×C8×C61—21no—
154C2×C8×C61—21no—
155C2×C8×C61—21no—
156C2×C8×C61—21no—
157C2×C8×C61—21no—
158C2×C8×C61—21no—
159C4⋊C4×C61—21no—
160C4⋊C4×C61—21no—
161C4⋊C4×C61—21no—
162C4⋊C4×C61—21no—
163C4⋊C4×C61—21no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—42no—
167C4⋊C4×C61—42no—
168C4⋊C4×C61#4112yes—
169C42×C61—81no—
170C42×C61C2×D412yes—
171C42×C61#4112yes—
172#11758198—24no—
173#11758198—22no—
174#11758198—22no—
175#11758198—81no—
176#11758198—81no—
177#11758198—81no—
178C4⋊Dic61—24no—
179C4⋊Dic61—21no—
180C4⋊Dic61—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61—21no—
185C4⋊Dic61—81no—
186C4⋊Dic61—81no—
187C4⋊Dic61—81no—
188#11758196—22no—
189#11758196—22no—
190#11758196—42no—
191#11758196—81no—
192#11758196—81no—
193C4×Dic61—21no—
194C4×Dic61—21no—
195C4×Dic61—42no—
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418C2×D412yes—
201C2×#92418C2×D412yes—
202C23×C61C22×D411yescharacteristic
203C22×D61—21no—
204C22×D61—21no—
205C22×D61—21no—
206C22×D61—21no—
207C22×D61—21no—
208C22×D61—21no—
209C22×D61—21no—
210C2×C4×C61—21no—
211C2×C4×C61—21no—
212C2×C4×C61—21no—
213C2×C4×C61—21no—
214C2×C4×C61—22no—
215C2×C4×C61—41no—
216C2×C4×C61—41no—
217C2×C4×C61—41no—
218C2×C4×C61—41no—
219C2×C4×C61—41no—
220C2×C4×C61—41no—
221C2×C4×C61—41no—
222C2×C4×C61—41no—
223C2×C4×C61—41no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61#12112yes—
227C2×C4×C61#12112yes—
228C2×C4×C61C22×D411yescharacteristic
229C2×C4×C61C2×#4111yescharacteristic
230C2×C4×C61C2×#4111yescharacteristic
231C2×C4×C61C2×#4111yescharacteristic
232C2×C4×C612−1+411yescharacteristic
233C2×C4×C612−1+411yescharacteristic
234C2×Dic61—21no—
235C2×Dic61—21no—
236C2×Dic61—21no—
237C2×Dic61—21no—
238C2×Dic61—22no—
239C2×Dic61—21no—
240C2×Dic61—21no—
241C2×Dic61—21no—
242C2×Dic61—21no—
243C2×Dic61—21no—
244C2×Dic61—41no—
245C2×Dic61—41no—
246C2×Dic61—41no—
247C2×Dic61—41no—
248C2×Dic61—41no—
249C2×Dic61—41no—
250C2×Dic61—41no—
251C2×Dic61—41no—
252C2×Dic61—41no—
253C2×Dic61—41no—
254C2×Dic61—41no—
255C4×D61—41no—
256C4×D61—41no—
257C4×D61—41no—
258C4×D61—41no—
259Dic122—22no—
260Dic122—22no—
261Dic122—41no—
262Dic122—41no—
263C8×C61—41no—
264C8×C61—41no—
265#92418—22no—
266#92418—22no—
267#24715—611nomaximal, Sylow
268C22×C61C2×#12111yescharacteristic
269C22×C61#52511yescharacteristic
270C22×C61#53611yescharacteristic
271C22×C61#57611yescharacteristic
272C22×C61#57711yescharacteristic
273C22×C61#57811yescharacteristic
274C22×C61#57811yescharacteristic
275C2×D61—41no—
276C2×D61—41no—
277C2×D61—41no—
278C2×D61—41no—
279C2×D61—41no—
280C2×D61—41no—
281C2×D61—41no—
282C4×C61—22no—
283C4×C61—22no—
284C4×C61—42no—
285C4×C61—81no—
286C4×C61—81no—
287C4×C61—81no—
288C4×C61#54711yescharacteristic
289C4×C61#54811yescharacteristic
290C4×C61#55211yescharacteristic
291C4×C61#55611yescharacteristic
292Dic61—42no—
293Dic61—41no—
294Dic61—41no—
295Dic61—41no—
296Dic61—81no—
297Dic61—81no—
298Dic61—81no—
299C2×#479—611no—
300C2×#433—611no—
301#2629—611no—
302#2323—611no—
303#2077—611no—
304#2075—611no—
305#2036—611no—
306#2036—611no—
307#1989D6111yescharacteristic, complemented
308#1947—611no—
309#1943—611no—
310#1942—611no—
311#1935—611no—
312#1933—611no—
313#1803—611no—
314C2×C61#241511yescharacteristic
315C2×C61#306111yescharacteristic
316C2×C61#306311yescharacteristic
317C2×C61#311911yescharacteristic
318C2×C61#312711yescharacteristic
319C2×C61#324211yescharacteristic
320C2×C61#324311yescharacteristic
321D61—81no—
322C2×#125C2×D6111yescharacteristic
323C2×C22⋊Q8—611no—
324C2×C4×Q8—611no—
325C2×#117—611no—
326#479—1224no—
327#433—1224no—
328C2×#107—611no—
329C2×#107—611no—
330C2×#107—611no—
331C2×#106—611no—
332C2×C4⋊C8—611no—
333C2×C4⋊C8C2×D6111yescharacteristic
334C2×#103—611no—
335C2×#103—611no—
336C2×#103—611no—
337C2×#103—611no—
338C2×C22⋊C8—611no—
339C2×C22⋊C8—611no—
340C2×#97—611no—
341C2×C4×C8—611no—
342#398—1221no—
343#398—1221no—
344#396—1221no—
345#396—1221no—
346#391—611no—
347#389—611no—
348#389—611no—
349#389—611no—
350#389—1221no—
351#388—1221no—
352#388—1221no—
353#387—1221no—
354#384—611no—
355#380—611no—
356#380—611no—
357#380—611no—
358C4×C4⋊C4C2×D6111yescharacteristic
359#340—611no—
360#340—611no—
361#340—611no—
362#340—611no—
363#340C2×D6111yescharacteristic
364#340C2×D6111yescharacteristic
365#340C2×D6111yescharacteristic
366#340C2×D6111yescharacteristic
367C61#2471511yescharacteristic, complemented, Sylow
368C22×Q8—611no—
369C23×C4—611no—
370C22×C8—611no—
371C22×C8—611no—
372C22×C8C22×D6111yescharacteristic
373C22×C8C22×D6111yescharacteristic
374#125—22no—
375#125—22no—
376C22⋊Q8—1222no—
377C22⋊Q8—1222no—
378C4×Q8—1222no—
379C4×Q8—1222no—
380#117—1222no—
381#117—1222no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—611no—
385C2×C4⋊C4—611no—
386C2×C4⋊C4—611no—
387C2×C4⋊C4—611no—
388C2×C4⋊C4—611no—
389C2×C4⋊C4—1221no—
390C2×C4⋊C4—1221no—
391C2×C4⋊C4—1221no—
392C2×C4⋊C4—1221no—
393C2×C4⋊C4—1221no—
394C2×C4⋊C4—1221no—
395C2×C4⋊C4—1221no—
396C2×C4⋊C4C22×D6111yescharacteristic
397C2×C4⋊C4C22×D6111yescharacteristic
398C2×C4⋊C4C22×D6111yescharacteristic
399C2×C4⋊C4C22×D6111yescharacteristic
400C2×C22⋊C4—611no—
401C2×C22⋊C4—611no—
402C2×C22⋊C4—1221no—
403C2×C22⋊C4—1221no—
404C2×C22⋊C4—1221no—
405C2×C22⋊C4—1221no—
406C2×C42—21no—
407C2×C42—611no—
408C2×C42—1221no—
409C2×C42C22×D6111yescharacteristic
410#107—1222no—
411#107—1222no—
412#107—1222no—
413#106—1222no—
414C4⋊C8—22no—
415C4⋊C8—614no—
416#103—1222no—
417#103—1222no—
418#103—1222no—
419#103—1222no—
420C22⋊C8—1222no—
421C22⋊C8—1222no—
422#97—1222no—
423C4×C8—1222no—
424#95—21no—
425#95—1221no—
426#95—1221no—
427#95—1221no—
428#95—1221no—
429#95—1221no—
430#95—1221no—
431#95—1221no—
432#95—1221no—
433C24—611no—
434C2×Q8—612no—
435C2×Q8—1221no—
436C2×Q8—1221no—
437C2×Q8—1221no—
438C2×Q8—1221no—
439C2×Q8—1221no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—611no—
445C22×C4—611no—
446C22×C4—611no—
447C22×C4—1221no—
448C22×C4—1221no—
449C22×C4—1221no—
450C22×C4—1221no—
451C22×C4—1221no—
452C22×C4—1221no—
453C22×C4—1221no—
454C22×C4—1221no—
455C22×C4—1221no—
456C22×C4—1221no—
457C22×C4D4×D6111yescharacteristic
458C22×C4D4×D6111yescharacteristic
459C22×C4C23×D6111yescharacteristic
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—612no—
467C2×C8—612no—
468C2×C8—1221no—
469C2×C8—1221no—
470C2×C8—1221no—
471C2×C8—1221no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—42no—
480C4⋊C4—42no—
481C4⋊C4—1224no—
482C4⋊C4—1222no—
483C4⋊C4—1222no—
484C4⋊C4—1221no—
485C4⋊C4—1221no—
486C4⋊C4—1221no—
487C4⋊C4—1221no—
488C4⋊C4—1221no—
489C4⋊C4—1221no—
490C4⋊C4—4881no—
491C4⋊C4—4881no—
492C4⋊C4—4881no—
493C4⋊C4—4881no—
494C4⋊C4—4881no—
495C4⋊C4—2442no—
496C4⋊C4#1175822612yes—
497C22⋊C4—1224no—
498C22⋊C4—1222no—
499C22⋊C4—1222no—
500C22⋊C4—4881no—
501C22⋊C4—4881no—
502C22⋊C4—4881no—
503C42—81no—
504C42—1221no—
505C42—1221no—
506C42—2442no—
507C42#1175822212yes—
508C42D4×D6112yes—
509C23—1221no—
510C23—1221no—
511C23—1221no—
512C23—1221no—
513C23—1221no—
514C23—1221no—
515C23—1221no—
516C23C2×D4×D6111yescharacteristic
517Q8—1222no—
518Q8—1222no—
519Q8—2441no—
520Q8—2441no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—22no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—1221no—
538C2×C4—1221no—
539C2×C4—1221no—
540C2×C4—1222no—
541C2×C4—1221no—
542C2×C4—1221no—
543C2×C4—1221no—
544C2×C4—1221no—
545C2×C4—1221no—
546C2×C4—1221no—
547C2×C4—2441no—
548C2×C4—2441no—
549C2×C4—2441no—
550C2×C4—2441no—
551C2×C4—2441no—
552C2×C4—2441no—
553C2×C4—2441no—
554C2×C4—2441no—
555C2×C4—2441no—
556C2×C4—2441no—
557C2×C4—2441no—
558C2×C4—2441no—
559C2×C4—2441no—
560C2×C4—2441no—
561C2×C4—2441no—
562C2×C4#1451975012yes—
563C2×C4#1451975012yes—
564C2×C4C2×D4×D6111yescharacteristic
565C2×C4#41×D6111yescharacteristic
566C2×C4C2×#1175822211yescharacteristic
567C2×C4C2×#1175822611yescharacteristic
568C2×C4#1451982411yescharacteristic
569C2×C4#1451982511yescharacteristic
570C8—41no—
571C8—41no—
572C8—1222no—
573C8—1222no—
574C22—2441no—
575C22—2441no—
576C22—2441no—
577C22—2441no—
578C22—2441no—
579C22—2441no—
580C22—2441no—
581C22C2×#1451975011yescharacteristic
582C22#1684027511yescharacteristic
583C22#1684033511yescharacteristic
584C22#1684056611yescharacteristic
585C22#1684056911yescharacteristic
586C22#1684057611yescharacteristic
587C22#1684057811yescharacteristic
588C4—22no—
589C4—22no—
590C4—42no—
591C4—81no—
592C4—81no—
593C4—81no—
594C4—4881no—
595C4—4881no—
596C4—4881no—
597C4—2441no—
598C4—2442no—
599C4—2441no—
600C4—2441no—
601C4#1684041511yescharacteristic
602C4#1684042011yescharacteristic
603C4#1684045311yescharacteristic
604C4#1684048511yescharacteristic
605C2—4881no—
606C2#2144925111yescharacteristic
607C2#2145548811yescharacteristic
608C2#2145551311yescharacteristic
609C2#2145602311yescharacteristic
610C2#2145612111yescharacteristic
611C2#2145708411yescharacteristic
612C2#2145710111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1989C2
socleC23×C61C22×D4
prime radicalC23×D61C2×D4
hypercenter#1989D61
hypocenterC61#24715
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1989

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#16840066C2semidirect
9. #21446577C2semidirect
10. #21446556C2semidirect
11. #21446551C2semidirect
12. #21446507C2semidirect
13. #21446493C2semidirect
14. #21445825C2semidirect
15. C61×#1989C2semidirect
307. #1989D61semidirect
367. C61#24715semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#168400662
C2×#168398222
#214516502
#214485022
#214472572
#214472462
#214470252
#214465772
#214465562
#214465512
#214465072
#214464932
#214458252
C61×#19892
#2471561